Question: Simplify the following expression: $q = \dfrac{-2p^2 - 14p + 16}{p + 8} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ q =\dfrac{-2(p^2 + 7p - 8)}{p + 8} $ Then we factor the remaining polynomial: $p^2 + {7}p {-8} $ ${8} {-1} = {7}$ ${8} \times {-1} = {-8}$ $ (p + {8}) (p {-1}) $ This gives us a factored expression: $\dfrac{-2(p + {8}) (p {-1})}{p + 8}$ We can divide the numerator and denominator by $(p - 8)$ on condition that $p \neq -8$ Therefore $q = -2(p - 1); p \neq -8$